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RESOLVER LAS ECUACIONES DIFERENCIALES POR EL MÉTODO DE SEPARACIÓN DE VARIABLES. 1. $x \cdot \operatorname{sen} x e^{-y} d x-y d y=0$ 2. $x \cdot \tan x d x-y \cdot \cos x d y=0$ 3. $(1+e^x) y \cdot y^{\prime}=e^x \quad y(0)=1$ 4. $x y^4 d x+(y^2+2) e^{-3 x} d y=0$ 5. $y^{\prime} \cdot \operatorname{sen} x=y \cdot \ln y$ 6. $(1+y^2) d x+(1+x^2) d y=0$ 7. $(y^2+x y^2) y^{\prime}+x^2-y x^2=0$ 8. $y \cdot \ln y d x+x d y=0$ 9. $y^{\prime}=a^{(x+y)} \quad a>0 ; a \neq 1$ 10. $y-x y^{\prime}=a \cdot(1+x^2 y^{\prime}) \quad$ DONDE a ES CONSTANTE. DEMOSTRAR EL PROCEDIMIENTO COMPLETO AL RESOLVER CADA UNA DE LAS ECUACIONES.

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draw a resonance structure for p-benzoquinone

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Training Questions Let $m$ be a positive integer and consider the computation of $I_m := \int_0^\pi f_m(x) dx,$ where $f_m(x) := \begin{cases} x^2, & \text{if } x < 1.0, \\ x^2 + (x - 1.0)^m, & \text{if } x \geq 1.0. \end{cases}$ Implement the composite Simpson's rule and perform the following two tasks: 1. Implement a Matlab function that approximates $I_m$ using composite Simpson's rule. Fix a value of $m \neq 3$ such that you can verify the theoretical rate of convergence of composite Simpson's rule. To do this, let $h = \frac{\pi - 0}{n}$ and use your code to approximate $I_m$ for different values of $n$. Then, based on your data, verify that the absolute error (you will need to compute the exact value of $I_m$) decays like $O(h^4)$ (plot the absolute error and the $O(h^4)$ curve in a single figure). Indicate why this choice of $m$ allows you to do so based on the theoretical estimates seen in class. 2. Special case $m = 3$: Find the exact value of $I_3$ and compute several approximations of this integral (using your code from part (a)) for different values of $n$. Based on your data, attempt to find a mathematical relationship between $h$ and the error. Aim for an error of the form $O(h^p)$. Use 'polyfit' to find $p$. Is this rate guaranteed by the smoothness of $f_3$? (Explain). NOTE: Make at least two plots (one for each part) and compare them.

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A curve that shows the least-cost combination of inputs needed to produce each level of output for given input prices is: Question 23 options: a long run average total cost curve an isoquant curve an isocost curve an expansion path

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C. Questions 1. If the calorimetry experiment was used to measure the heat of reaction for an endothermic process, what would have been different about the observed change in temperature?

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An object with mass m is moving along the x-axis according to the equation , where \alpha and \beta are positive constants. What is the magnitude of the net force on the object at time

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Does a complex tone with components of 1000 Hz, 2500 Hz, and 3000 Hz have a missing fundamental?

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Although rarely used, which of the following is an instrument the Fed has to conduct monetary policy? Multiple Choice The corporate income tax The tax on unearned income The discount rate The interest rate on Treasury bonds

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1 a) Find the discrete-time Fourier transform (DTFT), $X(e^{j\omega})$, of a sequence $x[n]$ given $x[n] = \begin{cases} 2^{n-4}, & 2 \le n \le 11, \\ 0, & \text{otherwise.} \end{cases}$ b) Find the discrete-time Fourier transform (DTFT), $X(e^{j\omega})$, of a sequence $x[n]$ given $x[n] = \begin{cases} 2^{n-4}, & 2 \le n \le 11, \\ 0, & \text{otherwise.} \end{cases}$

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You want to design a fiber Fabry-Perot cavity (see problem 6.4) that provides a transmission maximum with T=1 for light with Î»=498nm (assume orthogonal incidence and a transmission minimum for Î»=500nm with T=0.01 without any further maxima in between. (a) Calculate the mirror distance d of the Fabry-Perot interferometer. (b) What value for the finesse F is needed? (c) What reflectivity R is needed?

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ashley p.